In recent years, a quantum computer has been known as a computer based on a new concept involving the active use of fundamental principles of quantum mechanics, and can compute a certain specific question (such as prime factorization of large natural number) at an extremely high speed as compared with a current classical computer. Such a quantum computer uses a quantum two-level system which is called a quantum bit corresponding to a bit of the classical computer. Information handled by the quantum computer is input to a quantum bit element. The quantum bit element may be recognized, for example, as an atom having different quantum states, and hence two of the quantum states are used to store the information.
There are several candidates for the quantum two-level system, and among others, a solid element holds promise in view of quantum bit integration. In particular, a quantum bit element using a superconductive element has a significant lead over other solid elements because of, for example, its strong coherence.
An example of the superconductive quantum bit element for realizing quantum computation is a fundamental structure of a superconductive magnetic flux quantum bit element as illustrated in FIG. 2 (see Non-Patent Document 1). When an external magnetic flux close to a half-quantum magnetic flux is applied to a superconductive loop 201 having three Josephson junctions 202, the superconductive magnetic flux quantum bit element takes two specific states in which energy is minimum in a case where a persistent current circulating through the superconductive loop 201 is in a combination of two states, a clockwise state and a counterclockwise state. Thus, the illustrated superconductive magnetic flux quantum bit operates as an effective quantum two-level system, that is, a quantum bit.
Herein, it is to be noted that two-bit logical operation is essential so as to implement the quantum computation. Therefore, in order to realize the quantum computer, it is necessary to provide interaction between quantum bit elements by any method. When the quantum bit elements are integrated in the form of a quantum bit computing circuit (quantum computing circuit), it is necessary to introduce the interaction between the quantum bit elements and, thereby, to provide a computing gate operated by the condition between two quantum bit elements.
For example, a quantum bit computing circuit described in Non-Patent Document 1 has the superconductive magnetic flux quantum bit elements 301 and 302 coupled to each other (see Non-Patent Document 2). As illustrated in FIG. 3, the two superconductive magnetic flux quantum bit elements 301 and 302 partially share their loops and thereby magnetic coupling is established between the quantum bit elements.
As the coupling between the quantum bit elements, several examples are also proposed. Another one of the quantum bit computing circuits (see Non-Patent Document 3) is illustrated in FIG. 4. As shown in FIG. 4, a large Josephson junction 403 is provided in a loop common part of two superconductive magnetic flux quantum bit elements 401 and 402 to increase an inductance, thereby enhancing the interaction therebetween.
As illustrated in FIG. 5, Non-Patent Document 1 described earlier also discloses another quantum bit computing circuit in which a superconductive loop including a superconductive magnetic flux quantum interference device (SQUID) 504 is provided as a superconductive transformer 503 between superconductive magnetic flux quantum bit elements 501 and 502 to realize magnetic coupling between the superconductive magnetic flux quantum bit elements 501 and 502.
In a quantum bit computing circuit according to another technology related to this (see Non-Patent Document 4), as illustrated in FIG. 6, there is provided a superconductive transformer 603 in which two superconductive loops including superconductive magnetic flux quantum interference devices (SQUIDs) 604 are symmetrically coupled to each other to accomplish magnetic coupling between superconductive magnetic flux quantum bit elements 601 and 602. Further, in a quantum bit computing circuit according to another technology (see Non-Patent Document 5), as illustrated in FIG. 7, there is provided a superconductive transformer 703 in which a superconductive magnetic flux quantum interference device (SQUID) 704 is connected not in series but in parallel with a superconductive loop to realize magnetic coupling between the superconductive magnetic flux quantum bit elements 701 and 702.
In another quantum bit computing circuit (see Non-Patent Document 6), as illustrated in FIG. 8, a superconductive magnetic flux quantum interference device (SQUID) 803 which is current-biased is provided between superconductive magnetic flux quantum bit elements 801 and 802 to realize magnetic coupling between the superconductive magnetic flux quantum bit elements 801 and 802 through the superconductive magnetic flux quantum interference device (SQUID) 803.
In any of the quantum bit computing circuits, each of the quantum bit elements is required to maintain coherence for a long time. To be specific, it is known that the coherence of a quantum bit element greatly depends on a bias condition, and a long coherence time period is obtained just at an optimum operating point to which a half-quantum magnetic flux is applied (see Non-Patent Document 7).
Further, a quantum bit computing circuit similar to one of Non-Patent Document 6 is proposed also in Non-Patent Document 8. To describe more specifically, Non-Patent Document 8 discloses a quantum bit computing circuit in which a superconductive magnetic flux quantum interference device (SQUID) biased with a DC current is provided between two quantum bit elements having different characteristic frequencies in order to parametrically induce coupling between the two quantum bit elements. In this case, the superconductive magnetic flux quantum interference device (SQUID) is biased with a d.c. bias current selected in relation to a critical current. This structure can use a nonlinear inductance obtained when the superconductive magnetic flux quantum interference device (SQUID) is biased by d.c. current. The superconductive magnetic flux quantum interference device (SQUID) is given a microwave magnetic field pulse which has a frequency equal to a difference frequency between the respective characteristic frequencies of the two superconductive magnetic flux quantum bit elements, in order to induce coupling between the two quantum bit elements.
(Non-Patent Document 1)
“Josephson Persistent-Current Qubit” J. E. Mooij, T. P. Orlando, L. Levitov, L. Tian, C. H. van der Wal, and S. Lloyd, AUGUST 1999 VOL 285 SCIENCE p: 1036 (1999).
(Non-Patent Document 2)
“Spectroscopy on Two Coupled Superconducting Flux Qubits” J. B. Majer, F. G. Paauw, A. C. J. ter Haar, C. J. P. M. Harmans, and J. E. Mooij, PHYSICAL REVIEW LETTERS (PRL) 94, 090501 (2005).
(Non-Patent Document 3)
“Direct Josephson coupling between superconducting flux qubits” M. Grajcar, A. Izmalkov, S. H. W. van der Ploeg, S. Linzen, E. Il'ichev, Th. Wagner, U. Hubner, H.-G. Meyer, A. Maassen van den Brink, S. Uchaikin, and A. M. Zagoskin, PHYSICAL REVIEW B 72, 020503(R) 2005.(Non-Patent Document 4)“Tunable Transformer for Qubits Based on Flex States” T. V. Filippov, S. K. Tolpygo, J. Mannik, and J. E. Lukens, IEEE TRANSACTIONS ON APPLIED SUPERCONDUCTIVITY VOL. 13, NO. 2. JUNE p: 1005 (2003).(Non-Patent Document 5)“Controllable Flux Coupling for the Integration of Flux Qubits” C. Cosmelli, M. G. Castellano, F. Chiarello, R. Leoni, D. Simeone, G. Torrioli, P. Carelli, arXiv:cond-mat/0403690v1 29 Mar. 2004.(Non-Patent Document 6)“Entangling flux qubits with a bipolar dynamic inductance” B. L. T. Plourde, J. Zhang, K. B. Whaley, F. K. Wilhelm, T. L. Robertson, T. Hime, S. Linzen, P. A. Reichardt, C.-E. Wu, and J. Clarke, PHYSICAL REVIEW B 70, 140501(R) (2004).(Non-Patent Document 7)“Dephasing of a Superconducting Qubit Induced by Photon Noise” P. Bertet, I. Chiorescu, G. Burkard, K. Semba, C. J. P. M. Harmans, D. P. DiVincenzo, and J. E. Mooij, PHYSICAL REVIEW LETTERS (PRL) 95, 257002 (2005).(Non-Patent Document 8)“Parametric coupling for superconducting qubits” P. Bertet, C. J. P. M. Harmans, and J. E. Mooij, PHYSICAL REVIEW B 73, 064512 (2006).